Iterating MovingMap with Nest

I am trying to create a background correction inspired by the PyMca strip background method. The data I’m trying to correct is a HPLC chromatogram in the form of a TimeSeries (named normalizedchromatogram in this case). The idea is to generate a background through iterations of Mean and MovingMap with a windows size dependent on the MinimumTimeIncrement of said TimeSeries.
A code snippet thats already working as intended:

MovingMap[Mean, normalizedchromatogram, {10*MinimumTimeIncrement[normalizedchromatogram], Center}, "Fixed"]

However, I don’t know how to iterate this snippet now. It seems to me, that using Nest would be a suitable approach to iterate the code, but Nest doesn’t allow for using my code snippet above as a function.

Thanks in advance!